Certificate for #108 ⟨a, b, c | ab=a, bcb=1⟩

Back:⟨a, b, c | ab=a, bcb=1⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [5].

[2] bcb=1

Axiom: bcb=1.

Referenced by [3], [4], [6].

[3] acb=a

Overlap of [1] ab=a with [2] bcb=1:

a b bcb

Critical pair: a=acb.

Flip LHS and RHS.

Referenced by [5].

[4] cb=bc

Overlap of [2] bcb=1 with [2] bcb=1:

bc b bcb

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[5] ac=a

Simplify [3] acb=a.

Reduce LHS:

[4]a(cb)
[1]⇒ (ab)c
⇒ ac

Defines rule #2.

[6] bbc=1

Overlap of [2] bcb=1 with [4] cb=bc:

b cb cb

Critical pair: bbc=1.

Defines rule #4.